Pssolver: A Maple implementation to solve first order ordinary differential equations with Liouvillian solutions, Computer Physics Communications, vol.183, issue.10, pp.2313-2314, 2012. ,
Integrating first-order differential equations with Liouvillian solutions via quadratures: a semi-algorithmic method, Journal of Computational and Applied Mathematics, vol.182, issue.2, pp.327-332, 2005. ,
A uniform approach for the fast computation of matrix-type Padé approximants, SIAM J. Matrix Anal. Appl, vol.15, issue.3, pp.804-823, 1994. ,
, Progress in Theoretical Computer Science. Birkhäuser Boston Inc, vol.1, 1994.
Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields, Math. Comp, vol.85, issue.299, pp.1393-1425, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00871663
Fast computation ,
URL : https://hal.archives-ouvertes.fr/inria-00000960
, Annual ACM-SIAM Symposium on Discrete Algorithms, pp.1012-1021, 2007.
Complexity issues in bivariate polynomial factorization, Proceedings of ISSAC'04, pp.42-49, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00186759
Symbolic integration. I, volume 1 of Algorithms and Computation in Mathematics ,
Feuilletages singuliers de codimension un, groupo¨?degroupo¨?de de Galois et intégrales premì eres, Annales de l'Institut Fourier, vol.56, issue.3, pp.735-779, 2006. ,
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time, J. Complexity, vol.27, issue.2, pp.246-262, 2011. ,
Décomposition et intégralespremì eres rationnelles: algorithmes et complexité. Habilitation thesis, vol.3, 2014. ,
Bounding the number of remarkable values via Jouanolou's theorem, Journal of Differential Equations, vol.258, issue.10, pp.3535-3545, 2015. ,
Liouvillian first integrals of second order polynomial differential equations, Electron. J. Differential Equations, vol.7, issue.49, 1999. ,
Multiplicity of invariant algebraic curves in polynomial vector fields, Pacific J. Math, vol.229, issue.1, pp.63-117, 2007. ,
Mémoire sur leséquationsleséquations diff'´ erentielles du premier ordre et du premier degré, Bull. Sci. Math, vol.32, pp.151-200, 1878. ,
Analysing the structure of the integrating factors for first-order ordinary differential equations with Liouvillian functions in the solution, J. Phys. A, vol.35, issue.4, pp.1001-1006, 2002. ,
A method to tackle first-order ordinary differential equations with Liouvillian functions in the solution, J. Phys. A, vol.35, issue.17, pp.3899-3910, 2002. ,
Qualitative theory of planar differential systems. Universitext, 2006. ,
A new algorithm for finding rational first integrals of polynomial vector fields, Qual. Theory Dyn. Syst, vol.9, issue.1-2, pp.89-99, 2010. ,
Multiplicities of zeroes of polynomials on trajectories of polynomial vector fields and bounds on degree of nonholonomy, Math. Res. Lett, vol.2, issue.4, pp.437-451, 1995. ,
Modern computer algebra, 1999. ,
Integrability and nonintegrability of dynamical systems, Advanced Series in Nonlinear Dynamics, vol.19, 2001. ,
Computing minimal interpolation bases, Journal of Symbolic Computation, vol.83, pp.272-314, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01241781
, ´ Equations de Pfaff algébriques, vol.708
DOI : 10.1007/bfb0063393
, , 1979.
, Linear Algebra and Its Applications, 2015.
Sharp precision in Hensel lifting for bivariate polynomial factorization, Math. Comp, vol.75, issue.254, pp.921-933, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00186733
Computing closed form solutions of first order odes using the Prelle-Singer procedure, Journal of Symbolic Computation, vol.16, issue.5, pp.423-443, 1993. ,
A rational approach to the Prelle-Singer algorithm, J. Symbolic Comput, vol.24, issue.1, pp.31-43, 1997. ,
Vector fields, invariant varieties and linear systems, Ann. Inst. Fourier (Grenoble), vol.51, issue.5, pp.1385-1405, 2001. ,
, Sur les intégrales doubles de fonctions rationnelles dont tous les résidus sont nuls. Bulletin des sciences mathématiques, p.26, 1902.
Elementary first integrals of differential equations, Trans. Amer. Math. Soc, vol.279, issue.1, pp.215-229, 1983. ,
Algorithmic complexity of algebraic and geometric models, Theoret. Comput. Sci, vol.157, issue.1, pp.129-136, 1994. ,
, Reduzibilität Ebener Kurven. J. Reine Angew. Math, vol.369, pp.167-191, 1986.
Polynomials with special regard to reducibility, of Encyclopedia of Mathematics and its Applications, vol.77, 2000. ,
Elementary first integrals and algebraic invariant curves of differential equations, Exposition. Math, vol.11, issue.5, pp.433-454, 1993. ,
Liouvillian first integrals of differential equations, Trans. Amer. Math. Soc, vol.333, issue.2, pp.673-688, 1992. ,
Integrability of Dynamical Systems: Algebra and Analysis. Developments in Mathematics, 2017. ,
Efficient algorithms for order basis computation, J. Symbolic Comput, vol.47, issue.7, pp.793-819, 2012. ,
,
E-mail address: guillaume.cheze@math.univ-toulouse.fr T. Combot, 2009. ,